- An Introduction:
Soumendra Nath Thakur
February 08, 2025
In the framework of Extended Classical Mechanics (ECM),
"photon dynamics under negative apparent mass and effective
acceleration" describes the concept that photons, when viewed through
the lens of ECM, can be understood as possessing a negative apparent mass,
leading to an "effective acceleration" that counteracts the expected
gravitational pull, allowing them to travel at the speed of light seemingly
unimpeded by gravity; this phenomenon is explained by the unique dynamics
arising from the negative mass value in the equations of motion.
Key points about this concept:
Negative Apparent Mass:
Unlike regular matter with
positive mass, in ECM, photons are assigned a negative apparent mass, which
means they would behave differently under the influence of a force, effectively
experiencing a repulsive force instead of attraction.
Effective Acceleration:
Due to the negative
apparent mass, a photon experiences an "effective acceleration" that
is essentially a constant value, even when encountering gravitational fields. This
acceleration acts in a way that cancels out the gravitational pull, enabling
the photon to maintain its constant speed.
Interpretation:
This concept is not meant to suggest that
photons physically have negative mass, but rather that when analysing photon
dynamics within the ECM framework, the mathematical treatment results in a
negative apparent mass value, leading to unique behaviour.
How it relates to other physics concepts:
Special Relativity:
While ECM provides an
alternative perspective, it is important to note that the standard model of
physics, including special relativity, still holds that photons have zero rest
mass and travel at the speed of light.
Dark Energy:
Some researchers have explored potential
connections between the concept of negative apparent mass in ECM and the
mysterious phenomenon of dark energy, which is thought to be driving the
accelerating expansion of the universe
The Interplay of
Inertia, Apparent Mass, and Gravitational Potential:
In classical
mechanics, resistance to acceleration is attributed to inertia—an object's
inherent tendency to resist changes in motion, which is directly proportional
to its mass. This principle remains fundamental in Extended Classical Mechanics
(ECM); however, ECM extends the classical notion by introducing the concept of
negative apparent mass (-Mᵃᵖᵖ) in motion or gravitational potential differences.
Observationally, this concept finds support in the study by Chernin et al. (2013)
on the Coma cluster of galaxies, which demonstrates the large-scale influence
of dark energy as a repulsive gravitational effect. Their research suggests
that in certain cosmic environments, gravitationally repulsive behaviour
emerges, aligning with ECM’s framework where negative apparent mass modifies
the classical understanding of resistance and acceleration.
In ECM, an object's
resistance to acceleration is not solely determined by its classical inertial
mass but also by the interaction between inertial mass and negative apparent
mass. This interaction gives rise to an effective mass (Mᵉᶠᶠ) that can
transition between positive and negative values, depending on the influence of
motion or gravitational potential differences:
Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)
Mᵉᶠᶠ = -Mᵃᵖᵖ where Mᴍ =
0
At low velocities or
in weak gravitational fields, the system behaves classically, with a positive
effective mass.
In high-motion regimes
or strong gravitational potential differences, negative apparent mass
introduces a repulsive effect, modifying the system's resistance to
acceleration.
This interplay between
inertial mass, apparent mass and gravitational potential leads to a broader
understanding of resistance in ECM. Rather than solely relying on classical
inertia, ECM incorporates dynamic influences that may provide deeper insights
into gravitational interactions, repulsive forces, and potential connections to
dark matter and cosmic-scale phenomena.
Force Dynamics on
Photons:
• Derive the force
equation F = −Mᵃᵖᵖaᵉᶠᶠ for photons using apparent mass and associated
acceleration.
• Explore how this
equation governs the photon’s motion under varying energy-momentum conditions.
• The derivation of
the effective acceleration aᵉᶠᶠ aligns with the methodological exploration of
force and acceleration acting on photons. It would complement the discussion of
the force equation
F = −Mᵃᵖᵖaᵉᶠᶠ and
further clarify the dynamics of photons as analysed through the extended
classical mechanics framework. The constant effective acceleration: aᵉᶠᶠ = 6 ×
10⁸ m/s².
Determination of
Constant Effective Acceleration of Photons
The distance travelled
by the photon in 1 second is 3 × 10⁸ m, and that the acceleration is constant. The
expression for the distance travelled in the case of constant acceleration is
given by:
Δd = v₀Δt + (1/2)aᵉᶠᶠ(Δt)²
Where:
• Δd is the distance
travelled (3 × 10⁸ m in 1 second),
• v₀ is the initial velocity (0 m/s, at
emission),
• Δt is the time (1
second),
• aᵉᶠᶠ is the
effective acceleration, which we want to solve for.
Substituting the known
values into the equation:
3 × 10⁸ m = 0·1 s +
(1/2)aᵉᶠᶠ(1)²
aᵉᶠᶠ = 6 × 10⁸ m/s²
Extended Photon
Dynamics and Phases of Motion: Transition from Rest to Constant Velocity
• When considering a
photon's motion, its apparent mass is negative. As a result, its effective
acceleration leads to a force with a negative value. This behaviour is
different from that of ordinary matter, which always has a positive mass.
• The commonly
referenced distance that light travels in one second does not represent the
photon's actual path during that time. Instead, it marks the moment of
emission, where the photon, initially at rest in an apparent sense, rapidly attains
its full velocity within a brief interval.
• During this
transition period, the effective acceleration is determined by the relationship
between force and the negative apparent mass. The force involved does not come
from an external source but is instead exerted by the photon itself due to its
unique mass-energy properties. This results in the photon undergoing a
continuous deceleration at twice the speed of light.
• The force generated
by the photon serves a dual purpose. It counteracts the gravitational pull of
its source while ensuring the photon maintains a constant speed as it escapes.
The energy necessary for this process is provided by the photon itself,
allowing it to sustain the required acceleration and remain in
Photon Dynamics:
Returning to the Force Equation for Photons
• Since the apparent
mass is negative (−Mᵃᵖᵖ), the constant effective acceleration aᵉᶠᶠ = 6 × 10⁸
m/s² results in a force term with a negative value. This contrasts with the
behaviour of matter mass (Mᴍ), which always remains positive.
• The distance of 3 ×
10⁸ m in one second does not represent a photon’s trajectory over that
duration. Instead, it corresponds to the initial emission event, where the
photon, initially at rest in an apparent sense (t₀, v₀), attains a
velocity v₁ at time t₁, with Δt = t₁ − t₀ = 1 second and Δv = v₁ − v₀ = 3 × 10⁸
m/s².
• During this interval
(t₁ − t₀), the effective acceleration is
given by aᵉᶠᶠ = F/(−Mᵃᵖᵖ). The force F is not an external force but is instead
exerted by the photon itself due to its negative apparent mass (−Mᵃᵖᵖ). This
implies that the photon undergoes continuous deceleration at twice the speed of
light (6 × 10⁸ m/s²).
• The exerted force
(F) not only counteracts the gravitational attraction of the source (Fg) but
also enables the photon to escape the gravitational well at a constant speed of
3 × 10⁸ m/s². The energy required for this escape is compensated by the photon
itself, maintaining the necessary energy balance to sustain its effective
acceleration of 6 × 10⁸ m/s².
Explanation of Phases
of Motion: Transition from Rest to Constant Velocity
On a number line,
there are infinitely many points between any two nearest numbers. When you say
"1," you are actually referring to the difference between 0 and 1,
with an infinite sequence of points in between.
Similarly, while the
speed of light (c) appears constant on large scales, at an infinitesimally
small scale, it has a beginning due to transmission delay. This delay occurs
because motion progresses incrementally, however small, starting from absolute
rest (v = 0) before reaching c.
The first phase, where
velocity increases from 0 to c, represents acceleration. Motion does not begin
with an arbitrary velocity but transitions from rest. The first phase starts at
zero (v = 0) and progresses to an initial velocity (v), whereas successive
phases continue from an already established velocity (v = v) rather than
starting anew from v = 0.
Mathematical
Representation
Let v(t) represent the
velocity of the object as a function of time. In the first phase of motion:
Initial Phase (Acceleration)
The motion begins from
rest, so at t = 0, v(0) = 0. The velocity increases from v=0 to some initial
velocity v₁ = c, over
some time interval Δt₁. The
acceleration a(t) in this phase is given by:
a(t) = dv(t)/dt, where
v(t) = ∫a(t)dt
The velocity increases
gradually from 0 to c, so during this phase, the object undergoes acceleration.
Subsequent Phases (Constant
Velocity)
After reaching an
initial velocity v₁ = c,
successive phases of motion proceed at this established velocity. In these
phases, the velocity remains constant, so for t > Δt₁, we have:
v(t) = v₁ = c, a(t) = 0
In the subsequent
phases, the object continues with the velocity v = c, without starting from
rest or accelerating further.
Photon Frequency:
Continuous Analogous Waves vs. Discrete Digital Signals
Photon frequency is
not a discrete, step-like, binary signal. Unlike digital frequencies, which
exhibit distinct on-off states, photon frequency is continuous and behaves in
an analogy manner. It follows a smooth, incremental, and decimal-like wave
pattern within its energy packet.
While digital signals
transition between fixed values, a photon's frequency remains constant within
its wave-packet, forming an uninterrupted oscillatory motion. This continuous
wave behaviour implies that every phase of a photon’s wave structure inherently
represents alternating cycles of acceleration and deceleration, rather than discrete
jumps between states.
This suggests that the wave characteristics of a photon are not just propagating in a static manner but involve intrinsic dynamical changes at the quantum scale, reinforcing the idea that photon energy and momentum continuously adjust within their wave structure.
